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Donald Trump still leads Ben Carson in Iowa and Carly Fiorina in New Hampshire, new polls show

Hillary Clinton is the Democratic front-runner in Iowa while Bernie Sanders is up in New Hampshire

Washington (CNN)Donald Trump still leads the Republican pack in the two first two states in the presidential nominating contest, though Ben Carson is on his heels in Iowa and Carly Fiorina is close behind in New Hampshire.

New NBC News/Wall Street Journal/Marist polls out Sunday morning show Trump up in Iowa, with 24% support to Carson's 19%. Fiorina is third at 8%, former Florida Gov. Jeb Bush at 7%, and Texas Sen. Ted Cruz, Florida Sen. Marco Rubio and Louisiana Gov. Bobby Jindal at 6% each, according to the poll.

In New Hampshire, Trump remains in first place with 21% support to Fiorina's 16%, Bush's 11%,and Rubio and Carson each with 10% support.

But despite his leads, the polls reflect some slipping for Trump. A month ago, Trump had been up 16 points in New Hampshire, rather than the 5-point advantage he has now. And in Iowa, Trump had a 7-point lead over Carson a month ago, compared to 5 points now.

Also dropping: Ohio Gov. John Kasich. He was in second place at 12% in New Hampshire in late August, but his support has fallen to 6%, the latest survey found.

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The Democratic race is largely unchanged in Iowa and New Hampshire.

Hillary Clinton has maintained her edge in Iowa, where she's up with 47% support to Vermont Sen. Bernie Sanders' 36% and former Maryland Gov. Martin O'Malley's 4%.

The race changes, though, if Vice President Joe Biden is added. Then, Clinton is at 33% support to Sanders' 28% and Biden's 22%.

In New Hampshire, Sanders has kept his advantage. He's ahead of Clinton by nine percentage points, with 48% support to Clinton's 39%.

With Biden added, Sanders' lead is 42% to Clinton's 28% and Biden's 18%.

The poll was conducted September 23-30. Among Iowa Republicans, the margin of error is plus or minus 4.7 percentage points. It's 4.6 points with New Hampshire GOP voters. Among Democratic voters, it's 5.3 points in Iowa and 4 points in New Hampshire.